Determina el vértice, el dominio y rango de la función cuadrática: \[ f(x)=-x^{2}+10 x-30 \]

Find the domain of the function. \[ g(x)=\log _{2}\left(\frac{x-8}{x}\right) \] The domain is (Type your answer in interval notation.)

Find the domain of the function. \( g(x)=3-7 \log _{6}\left[\frac{x}{7}-8\right] \) The domain of \( g \) is (Type your answer in interval notation.)

Find the domain of the function. \( F(x)=\log _{6} x^{3} \) The domain of \( F \) is (Type your answer in interval notation.)

12. Nilai dari \( \frac{{ }^{2} \log 3 .{ }^{5} \log 32 \cdot{ }^{3} \log 5}{{ }^{5} \log \frac{1}{25}} \) adalah .... A. \( -\frac{5}{2} \) B. \( \frac{32}{25} \) C. \( -\frac{5}{25} \) D. \( \frac{5}{2} \) E. \( -\frac{2}{5} \)

Suppose that the function \( g \) is defined, for all real numbers, as follows. \( g(x)=\left\{\begin{array}{ll}-\frac{1}{4} x-2 & \text { if } x \leq-2 \\ (x-1)^{2}-2 & \text { if }-2<x \leq 2 \\ 4 & \text { if } x>2\end{array}\right. \) \( g(-3), g(0) \), and \( g(2) \). \( g(0)=\square \)